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Colored diff for /texts/archimedes/xml/Attic/valer_centr_01_la_1604.xml between version 1.8 and 1.9

version 1.8, 2002/07/31 14:04:15 version 1.9, 2002/08/05 20:41:03
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 <s>Dico pun&shy;<lb/>ctum E, e&longs;se figur&aelig; AB, centrum grauitatis. </s> <s>Dico pun&shy;<lb/>ctum E, e&longs;se figur&aelig; AB, centrum grauitatis. </s>
  
 <s>Si enim <lb/>E, non e&longs;t, erit aliud, e&longs;to F: &amp; iuncta EF producatur, <lb/>&amp; &longs;umatur in illa extra figur&aelig; AB, terminum, quodlibet <lb/>punctum G; &amp; vt e&longs;t FE, ad EG, ita &longs;it alia magnitudo <lb/>K, ad figuram AB, &amp; <lb/>ex vi hypothe&longs;is &longs;it pars <lb/>qu&aelig;dam CD, figur&aelig; <lb/>AB, cuius centrum gra <lb/>uitatis E, talis vt abla&shy;<lb/>ta relinquat AC, minus <lb/>magnitudine <emph type="italics"/>K.<emph.end type="italics"/> Mi&shy;<lb/>nor igitur proportio erit <lb/>AC, ad AB, qu&agrave;m K, <lb/>ad AB, hoc e&longs;t qu&agrave;m <lb/>FE, ad EG; fiat vt <lb/>AC, ad AB, ita EF, <lb/>ad FGH: &longs;ed F, e&longs;t cen <lb/>trum grauitatis totius <lb/>AB, &amp; E, vnius par&shy;<lb/>tis CD; reliqu&aelig; igitur <lb/><figure id="fig47"></figure><lb/>partis AC, centrum grauitatis erit H, vltra punctum G: &longs;ed <lb/>G, cadit extra terminum figur&aelig; AC; multo igitur magis H: <lb/>Quod e&longs;t ab&longs;urdum. </s> <s>Si enim <lb/>E, non e&longs;t, erit aliud, e&longs;to F: &amp; iuncta EF producatur, <lb/>&amp; &longs;umatur in illa extra figur&aelig; AB, terminum, quodlibet <lb/>punctum G; &amp; vt e&longs;t FE, ad EG, ita &longs;it alia magnitudo <lb/>K, ad figuram AB, &amp; <lb/>ex vi hypothe&longs;is &longs;it pars <lb/>qu&aelig;dam CD, figur&aelig; <lb/>AB, cuius centrum gra <lb/>uitatis E, talis vt abla&shy;<lb/>ta relinquat AC, minus <lb/>magnitudine <emph type="italics"/>K.<emph.end type="italics"/></s><s> Mi&shy;<lb/>nor igitur proportio erit <lb/>AC, ad AB, qu&agrave;m K, <lb/>ad AB, hoc e&longs;t qu&agrave;m <lb/>FE, ad EG; fiat vt <lb/>AC, ad AB, ita EF, <lb/>ad FGH: &longs;ed F, e&longs;t cen <lb/>trum grauitatis totius <lb/>AB, &amp; E, vnius par&shy;<lb/>tis CD; reliqu&aelig; igitur <lb/><figure id="fig47"></figure><lb/>partis AC, centrum grauitatis erit H, vltra punctum G: &longs;ed <lb/>G, cadit extra terminum figur&aelig; AC; multo igitur magis H: <lb/>Quod e&longs;t ab&longs;urdum. </s>
  
 <s>Non igitur aliud punctum &agrave; puncto <lb/>E; punctum igitur E, figur&aelig; AB, erit centrum grauitatis <lb/>Quod demon&longs;trandum erat. </s></p><pb pagenum="77"/><p type="head"> <s>Non igitur aliud punctum &agrave; puncto <lb/>E; punctum igitur E, figur&aelig; AB, erit centrum grauitatis <lb/>Quod demon&longs;trandum erat. </s></p><pb pagenum="77"/><p type="head">
  
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 <s>E&longs;to hemi&longs;ph&aelig;rio, vel hem&longs;ph&aelig;roidi ABC, cuius axis <lb/>BD, circum&longs;criptus cylindrus, vel portio cylindrica AF: <lb/>&amp; ponatur D<emph type="italics"/>K<emph.end type="italics"/> ip&longs;ius <emph type="italics"/>K<emph.end type="italics"/>B tripla. </s> <s>E&longs;to hemi&longs;ph&aelig;rio, vel hem&longs;ph&aelig;roidi ABC, cuius axis <lb/>BD, circum&longs;criptus cylindrus, vel portio cylindrica AF: <lb/>&amp; ponatur D<emph type="italics"/>K<emph.end type="italics"/> ip&longs;ius <emph type="italics"/>K<emph.end type="italics"/>B tripla. </s>
  
 <s>Dico reliqui ex &longs;oli-<pb pagenum="51"/>do AF dempto ABC, centrum grauitatis e&longs;&longs;e <emph type="italics"/>K.<emph.end type="italics"/> Nam <lb/>&longs;uper ba&longs;im circulum, vel ellip&longs;im, cuius diameter EF &longs;i&shy;<lb/>milem, &amp; oppo&longs;itam &longs;olidi ABC, vel AF ba&longs;i, cuius dia&shy;<lb/>meter AC, &longs;tet cylindrus, vel portio cylindrica EDF: vt <lb/>&longs;itaxis BD communis quatuor &longs;olidis ABC, EDF, <lb/>AF, &amp; reliqu&aelig; figur&aelig; dempto &longs;olido ABC compre&shy;<lb/>hen&longs;&aelig; &longs;uperficie cylindrica, &amp; circulo, vel ellip&longs;e circa EF, <lb/>&amp; dimidia &longs;uper&longs;icie &longs;ph&aelig;rica interiori, cuius figur&aelig; &longs;oli&shy;<lb/>d&aelig; ponimus centrum grauitatis <emph type="italics"/>K.<emph.end type="italics"/> Secto igitur axe <lb/>BD bifariam, &amp; &longs;ingulis eius partibus rur&longs;us bifariam, <lb/>ducti&longs;que per puncta &longs;ectionum planis quibu&longs;dam planis <lb/><figure id="fig145"></figure><lb/>pr&aelig;dictarum ba&longs;ium oppofitarum parallelis, &longs;ecta &longs;int qua&shy;<lb/>tuor pr&aelig;dicta &longs;olida, quorum, excepto propo&longs;ito re&longs;iduo, <lb/>&longs;ectiones omnes erunt circuli<gap/>, vel ellip&longs;es inter &longs;e &longs;imi&shy;<lb/>les, &amp; in &longs;olido AF etiam &aelig;quales, quarum omnium <lb/>diametri eiu&longs;dem rationis erunt in eodem plano, in quo <lb/>&longs;it parallelogrammum per axim AEFC: &longs;olidiautem dicti <lb/>re&longs;idui &longs;ectiones, re&longs;idua &longs;ectionum &longs;olidi ABC. </s> <s>Dico reliqui ex &longs;oli-<pb pagenum="51"/>do AF dempto ABC, centrum grauitatis e&longs;&longs;e <emph type="italics"/>K.<emph.end type="italics"/></s><s> Nam <lb/>&longs;uper ba&longs;im circulum, vel ellip&longs;im, cuius diameter EF &longs;i&shy;<lb/>milem, &amp; oppo&longs;itam &longs;olidi ABC, vel AF ba&longs;i, cuius dia&shy;<lb/>meter AC, &longs;tet cylindrus, vel portio cylindrica EDF: vt <lb/>&longs;itaxis BD communis quatuor &longs;olidis ABC, EDF, <lb/>AF, &amp; reliqu&aelig; figur&aelig; dempto &longs;olido ABC compre&shy;<lb/>hen&longs;&aelig; &longs;uperficie cylindrica, &amp; circulo, vel ellip&longs;e circa EF, <lb/>&amp; dimidia &longs;uper&longs;icie &longs;ph&aelig;rica interiori, cuius figur&aelig; &longs;oli&shy;<lb/>d&aelig; ponimus centrum grauitatis <emph type="italics"/>K.<emph.end type="italics"/></s><s> Secto igitur axe <lb/>BD bifariam, &amp; &longs;ingulis eius partibus rur&longs;us bifariam, <lb/>ducti&longs;que per puncta &longs;ectionum planis quibu&longs;dam planis <lb/><figure id="fig145"></figure><lb/>pr&aelig;dictarum ba&longs;ium oppofitarum parallelis, &longs;ecta &longs;int qua&shy;<lb/>tuor pr&aelig;dicta &longs;olida, quorum, excepto propo&longs;ito re&longs;iduo, <lb/>&longs;ectiones omnes erunt circuli<gap/>, vel ellip&longs;es inter &longs;e &longs;imi&shy;<lb/>les, &amp; in &longs;olido AF etiam &aelig;quales, quarum omnium <lb/>diametri eiu&longs;dem rationis erunt in eodem plano, in quo <lb/>&longs;it parallelogrammum per axim AEFC: &longs;olidiautem dicti <lb/>re&longs;idui &longs;ectiones, re&longs;idua &longs;ectionum &longs;olidi ABC. </s>
  
 <s>At circa <lb/><expan abbr="c&otilde;munes">communes</expan> axes inter &longs;e &aelig;quales &longs;egmenta axis BD, &amp; inter <lb/><expan abbr="ead&etilde;">eadem</expan> plana parallela, &longs;uper ba&longs;es &longs;ectiones duorum &longs;olido&shy;<lb/>rum ABC, EDF, cylindri, vel portiones cylindric&aelig; con&shy;<lb/>&longs;i&longs;tant altitudine, &amp; multitudine &aelig;quales; ita vt duarum fi&shy;<lb/>gurarum ex ijs compofitarum altera fit cirdum&longs;cripta &longs;oli&shy;<pb pagenum="52"/>do EDF, altera &longs;olido ABC in&longs;cripta. </s> <s>At circa <lb/><expan abbr="c&otilde;munes">communes</expan> axes inter &longs;e &aelig;quales &longs;egmenta axis BD, &amp; inter <lb/><expan abbr="ead&etilde;">eadem</expan> plana parallela, &longs;uper ba&longs;es &longs;ectiones duorum &longs;olido&shy;<lb/>rum ABC, EDF, cylindri, vel portiones cylindric&aelig; con&shy;<lb/>&longs;i&longs;tant altitudine, &amp; multitudine &aelig;quales; ita vt duarum fi&shy;<lb/>gurarum ex ijs compofitarum altera fit cirdum&longs;cripta &longs;oli&shy;<pb pagenum="52"/>do EDF, altera &longs;olido ABC in&longs;cripta. </s>
  

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